Methods and apparatus for mechanical resonating structures

ABSTRACT

Mechanical resonating structures and related methods are described. The mechanical resonating structures may provide improved efficiency over conventional resonating structures. Some of the structures have lengths and widths and are designed to vibrate in a direction approximately parallel to either the length or width. They may have boundaries bounding the length and width dimensions, which may substantially align with nodes or anti-nodes of vibration.

RELATED APPLICATIONS

The present application claims the benefit under 35 U.S.C. §119(e) ofU.S. Provisional Patent Application Ser. No. 61/177,706 filed May 13,2009 entitled “Methods and Apparatus for Mechanical ResonatingStructures”, which is hereby incorporated herein by reference in itsentirety.

BACKGROUND

1. Field

The technology described herein relates to mechanical resonatingstructures.

2. Related Art

Some resonators include a mechanical structure configured to vibrate inat least one dimension. Some typical mechanical resonators are capableof vibrating in multiple dimensions (e.g., two or three dimensions), andare capable of exhibiting various vibration modes. Some such mechanicalresonators are plate-shaped, and are planar. In some of the vibrationmodes, the plate-shaped planar mechanical resonator vibrates primarilyin one dimension (e.g., in an x-direction), but also exhibits lesser,secondary vibration in at least one other dimension (e.g., in ay-direction and/or a z-direction). The larger vibration in the onedimension (e.g., the x-direction) may be the desirable vibration, whilethe vibration in the other dimensions may be a consequence of thedesired vibration.

SUMMARY

Mechanical resonating structures and related methods are described.

According to one aspect, a device comprises a substantially planarmechanical resonating structure having a length and a width. Themechanical resonating structure is operable to exhibit primary vibrationhaving a direction approximately parallel to the length of themechanical resonating structure and secondary vibration having adirection approximately parallel to the width of the mechanicalresonating structure. Sides of the mechanical resonating structuresubstantially align with nodes of the secondary vibration for aresonance frequency of the mechanical resonating structure.

According to another aspect, a device comprises a substantially planarsuspended mechanical resonating structure comprising a piezoelectricmaterial. The mechanical resonating structure has a length and a width,and is coupled to a substrate by one or more anchors contacting sides ofthe mechanical resonating structure. The mechanical resonating structureis configured to support plate acoustic modes of vibration in which themechanical resonating structure exhibits primary vibration having adirection approximately parallel to the length of the mechanicalresonating structure and secondary vibration having a directionapproximately parallel to the width of the mechanical resonatingstructure. The primary vibration has a magnitude at least two timeslarger than a magnitude of the secondary vibration. Ends of themechanical resonating structure substantially align with anti-nodes ofthe primary vibration. Sides of the mechanical resonating structuresubstantially align with nodes of the secondary vibration. At least oneof the one or more anchors contacts the mechanical resonating structureat a point lying substantially on a node of the primary vibration and anode of the secondary vibration.

According to another aspect, a device comprises a mechanical resonatingstructure having a periphery lying substantially within a first plane,the periphery formed of one or more segments, wherein each of the one ormore segments substantially aligns with either a node or anti-node ofvibration of a resonance mode of the mechanical resonating structure.

According to another aspect, a device comprises a mechanical resonatingstructure configured to exhibit plate acoustic modes of vibration inwhich the mechanical resonating structure vibrates in a primarydirection and a secondary direction. The device further comprises ananchor interconnecting the mechanical resonating structure to a body,the anchor positioned to contact the mechanical resonating structure ata point positioned approximately on a node of vibration of themechanical resonating structure in the secondary direction.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects of the technology will be described with reference tothe following figures. It should be appreciated that the figures are notnecessarily drawn to scale. Also, the same reference number appearing inmultiple figures refers to the same item.

FIG. 1 illustrates a device comprising a mechanical resonating structureconnected to a substrate by two anchors, according to one embodiment ofthe technology described herein.

FIG. 2 illustrates the mechanical resonating structure shown in FIG. 1.

FIGS. 3A-3C illustrate an example of nodal behavior for a same frequencyof vibration in two dimensions on the mechanical resonating structure ofFIG. 1, according to one embodiment.

FIG. 4 is a flowchart of a method for determining the dimensions of amechanical resonating structure, according to one non-limitingembodiment.

FIG. 5 illustrates a portion of a mechanical resonating structurecomprising an electrode, according to one embodiment.

FIG. 6 illustrates the electric potential associated with a mechanicalresonating structure comprising an electrode, according to oneembodiment.

FIG. 7 illustrates a top-down view of a mechanical resonating structurehaving beveled edges, according to one embodiment.

DETAILED DESCRIPTION

Mechanical resonating structures and related methods are described.According to some aspects, a mechanical resonating structure exhibitsprimary vibration in the direction of (or approximately parallel to,which includes exactly parallel to) its length (e.g., an x-direction)and secondary vibration in the direction of its width. The width may bechosen to minimize the amount of displacement associated with thesecondary vibration at the width boundaries. Accordingly, the efficiencyof the mechanical resonating structure may be improved. According tosome aspects, anchors connect the mechanical resonating structure to abody (e.g., a substrate, or any other suitable type of body, which insome situations may be fixed). The anchors may be positioned to optimizetheir impact on the primary vibration of the mechanical resonatingstructure (e.g., to minimize their impact in some embodiments, or tomaximize their impact in other embodiments).

The aspects described above, as well as additional aspects, will now bedescribed in greater detail. These aspects may be used individually, alltogether, or in any combination of two or more.

FIG. 1 illustrates a device 100 comprising a mechanical resonatingstructure 102, having a length L, width W, and thickness T, coupled to abody 104 (e.g., a silicon substrate, or any other suitable body) by twoanchors 106 a and 106 b. In some embodiments, the length L is at leastone and half times as large as the width W, although not all embodimentsare limited in this respect. The mechanical resonating structure 102 issubstantially planar, but not all embodiments of the present technologyare limited to using planar resonating structures. Although coupled bythe anchors 106 a and 106 b, the mechanical resonating structure 102 isotherwise separated from the body 104 by an air gap 108, and thereforeis a suspended mechanical resonating structure.

The mechanical resonating structure 102 may vibrate in multipledimensions. For example, the mechanical resonating structure may beconfigured to vibrate primarily in a direction approximately parallel toits length, i.e., approximately in the x-direction in FIG. 1. In someoperating scenarios, although it may be desired for the mechanicalresonating structure to only vibrate along its length, such vibrationmay also result in vibration approximately parallel to the width (e.g.,vibration approximately in the y-direction in the non-limiting exampleof FIG. 1) and/or thickness (e.g., vibration approximately in thez-direction in the non-limiting example of FIG. 1). For example, if themechanical resonating structure is configured to support plate acousticmodes of vibration (i.e., any two-dimensional or three-dimensional modesof vibration; e.g., Lamb waves), vibration approximately parallel to thelength may give rise to vibration approximately parallel to the widthand/or thickness. According to some embodiments, vibration“approximately parallel” to a direction includes vibration exactlyparallel to the direction.

In some embodiments, the vibration in the primary direction (e.g., thex-direction in this non-limiting example) is greater than the vibrationin the y- and/or z-directions. For purposes of this application, suchvibration is referred to as “primary vibration” whereas the smallervibration is referred to as “secondary vibration.” In some embodiments,the magnitude of the primary vibration is at least two times greaterthan the magnitude of the secondary vibration. In some embodiments, themagnitude of the primary vibration is at least four times greater thanthe magnitude of the secondary vibration (e.g., at least 10 timesgreater, between 10 and 100 times greater, etc.). In some embodiments,the magnitude of the primary vibration is approximately four timesgreater than the secondary vibration. According to some embodiments, themagnitude of the primary vibration is between approximately two and sixtimes greater than the magnitude of the secondary vibration (e.g., threetimes greater, four times greater, any other suitable amount within thisrange). Thus, the various embodiments described herein involving primaryand secondary vibration are not limited to the primary vibration beinggreater than the secondary vibration by any particular amount.

According to one aspect of the technology described herein, mechanicalresonating structures configured to exhibit primary and secondaryvibration within a plane are dimensioned to minimize any impact of thesecondary vibration on the primary vibration. The secondary vibrationmay impact the efficiency of the mechanical resonating structure, andtherefore aspects of the technology described herein minimize the impactof the secondary vibration on the efficiency of the mechanicalresonating structure. A non-limiting example is now described withrespect to the mechanical resonating structure 102 of FIG. 1, which isillustrated in FIG. 2.

The mechanical resonating structure 102 shown in FIG. 2 may bedimensioned to reduce the impact of secondary vibration having adirection approximately parallel to the width on primary vibrationhaving a direction approximately parallel to the length direction. Asshown, the length L of the mechanical resonating structure 102 isbounded by the two ends, 202 a and 202 b. The width W is bounded by thetwo sides 204 a and 204 b. The mechanical resonating structure may beconfigured or excited to exhibit primary vibration having a directionapproximately parallel to the length L, i.e., approximately in thex-direction in the non-limiting example of FIG. 2. However, such primaryvibration may be accompanied by secondary vibration having a directionapproximately parallel to the width W, i.e., approximately in they-direction in FIG. 2. While such secondary vibration has not beenconventionally considered in designing mechanical resonating structuresof the general type shown in FIG. 2, Applicants have appreciated thatthis secondary vibration sometimes impacts the primary vibration of themechanical resonating structure, for example by reducing the efficiency(e.g., the Q factor) of such structures. Applicants have furtherappreciated that the impact of the secondary vibration may be reduced oreliminated by substantially aligning the sides 204 a and 204 b withnodes of the secondary vibration. Thus, according to one non-limitingembodiment, the width W is chosen such that the sides 204 a and 204 bsubstantially align with nodes of any secondary vibration in they-direction. According to some embodiments, one or both of the sides maybe positioned within approximately Λ/5 of a node of the secondaryvibration, where Λ is the length of a period of displacement in thedirection of secondary vibration, which may depend on the wavelength ofprimary vibration (e.g., FIG. 3B, described below, illustrates a singleperiod of displacement in the direction of secondary vibration).According to some embodiments, one or both of the sides may bepositioned within approximately Λ/8 of a node of the secondaryvibration. According to some embodiments, one or both of the sides maybe positioned within approximately Λ/9 of a node of the secondaryvibration. According to some embodiments, one or both of the sides maybe positioned within approximately Λ/12 of a node of the secondaryvibration.

According to some embodiments, the length L of the mechanical resonatingstructure 102 is chosen to promote vibration in the direction of thelength. For example, according to some embodiments, the length L of themechanical resonating structure 102 is chosen so the ends 202 a and 202b substantially align with anti-nodes of vibration in the direction ofthe length, i.e., in the x-direction in the non-limiting example of FIG.2.

According to some embodiments, both the length and the width may havevalues which enhance the efficiency of the mechanical resonatingstructure when exhibiting primary vibration approximately parallel tothe length. For example, the ends 202 a and 202 b may be positioned tosubstantially align with anti-nodes of vibration in the direction of thelength while the sides 204 a and 204 b may be positioned tosubstantially align with nodes of vibration in the direction of thewidth. Thus, according to some non-limiting embodiments, the entireperiphery (i.e., ends 202 a and 202 b, and sides 204 a and 204 b) of themechanical resonating structure in the xy plane substantially alignswith nodes and anti-nodes of vibration of the structure. The peripherymay be formed of one or more segments (e.g., ends 202 a and 202 b, andsides 204 a and 204 b), one or more of which may substantially alignwith anti-nodes of vibration while one or more may substantially alignwith nodes of vibration. Other configurations are also possible.

FIGS. 3A-3C provide a non-limiting example of the positioning of theperiphery of a mechanical resonating structure relative to primary andsecondary vibration nodes and anti-nodes, according to one embodiment.Specifically, FIGS. 3A-3C are plots of the normalized magnitude ofdisplacement of the mechanical resonating structure 102 for onenon-limiting mode of vibration, and thus show the nodal behavior of themechanical resonating structure in this non-limiting example. FIGS.3A-3C all relate to the same frequency of vibration. In FIGS. 3A-3B, thegrayscale is from −1 (i.e., negative maximum displacement in thisnon-limiting embodiment, represented by black) to 1 (i.e., positivemaximum displacement in this non-limiting embodiment, represented bywhite), with gray representing zero displacement. Thus, in FIGS. 3A-3B,black and white represent anti-nodes, while gray represents a node. InFIG. 3C, the grayscale is from 0 (i.e., minimum displacement in thisnon-limiting embodiment, represented by black) to 1 (i.e., maximumdisplacement in this embodiment, represented by white). Thus, in FIG.3C, white represents anti-nodes and black represents a node.

FIG. 3A illustrates the normalized displacement magnitude within themechanical resonating structure for a mode of primary vibration havingone period of vibration in the x-direction, i.e., along the length ofthe structure in this non-limiting example. Thus, the nodalconfiguration for this mode of vibration may be seen in the figure. Thenodes of the x-direction primary vibration are represented by lines 302a and 302 b. Anti-nodes of the x-direction primary vibration arerepresented by lines 304 a-304 c.

FIG. 3B illustrates the normalized displacement magnitude within themechanical resonating structure for secondary vibration corresponding tothe primary vibration of FIG. 3A (i.e., for the same frequency ofvibration as that of FIG. 3A). The nodal configuration for the secondaryvibration can be seen in FIG. 3B. The nodes of the y-direction vibrationare represented by lines 306. Thus, as shown, the sides 204 a and 204 bof the mechanical resonating structure substantially align with nodes ofthe y-direction vibration in the non-limiting example of FIG. 3B. Theanti-nodes 308 a-308 d lie substantially at the center of four quadrantsof the mechanical resonating structure.

FIG. 3C illustrates the total normalized displacement of the mechanicalresonating structure for the mode of vibration of FIGS. 3A-3B, i.e.,accounting for the displacement from the primary vibration of FIG. 3Aand the secondary vibration of FIG. 3B. Thus, because the totaldisplacement is not negative, the grayscale in FIG. 3C goes from 0(i.e., minimum displacement (nodes), shown by black) to 1 (i.e., maximumdisplacement (anti-nodes), shown by white). As will be described, insome embodiments a mechanical resonating structure may be coupled to abody by one or more anchors. In some such embodiments, the anchors maybe positioned at nodes of the total displacement, e.g., at the nodesillustrated in FIG. 3C.

It should be appreciated from the discussion of FIGS. 1-3C that variousaspects of the technology may apply to various types of mechanicalresonating structures. Therefore, the various aspects described hereinare not limited to use with any particular type of mechanical resonatingstructures. Rather, the mechanical resonating structure may comprise orbe formed of various materials, may be a single or multi-layeredstructure, may take various shapes, including straight-edged shapes andshapes with beveled edges (described further below), may have anysuitable absolute dimensions, may have any operational frequency rangeand desired resonance frequency, and may be actuated and/or detected inany suitable manner.

For example, the various aspects described herein may apply tomechanical resonating structures comprising or formed of any suitablematerial(s) and having any composition. According to some embodiments,the mechanical resonating structure may comprise or be formed of apiezoelectric material. According to some embodiments, the mechanicalresonating structure comprises silicon. According to some embodiments,the mechanical resonating structure comprises quartz, LiNbO₃, LiTaO₃,aluminum nitride (AlN), or any other suitable piezoelectric material(e.g., zinc oxide (ZnO), cadmium sulfide (CdS), lead titanate (PbTiO₃),lead zirconate titanate (PZT), potassium niobate (KNbO₃), Li₂B₄O₇,langasite (La₃Ga₅SiO₁₄), gallium arsenside (GaAs), barium sodiumniobate, bismuth germanium oxide, indium arsenide, indium antimonide),either in substantially pure form or in combination with one or moreother materials. Moreover, in some embodiments in which the mechanicalresonating structure comprises a piezoelectric material, thepiezoelectric material may be single crystal material. According to someembodiments, the mechanical resonating structure comprises one or morematerials (e.g., in the form of layers or otherwise) that providetemperature compensation functionality, for example to compensate fortemperature induced changes in the resonance behavior of the mechanicalresonating structure. Examples of such structures are described in U.S.Pat. App. Ser. No. 61/138,171, filed Dec. 17, 2008 and titled“Mechanical Resonating Structures Including a Temperature CompensationStructure,” and U.S. patent application Ser. No. 12/639,161, filed Dec.16, 2009 entitled “Mechanical Resonating Structures Including aTemperature Compensation Structure”, both of which are incorporatedherein by reference in their entireties. According to some embodiments,the mechanical resonating structure may be partially or fullytemperature compensated.

According to some embodiments, the mechanical resonating structurecomprises or is formed of multiple layers, making the structure acomposite structure. For example, the mechanical resonating structuremay comprise a base on which electrodes are formed. In addition, thebase may itself comprise one or more layers of differing materials,shapes, and/or thicknesses.

The mechanical resonating structures described herein may have anysuitable dimensions. According to some embodiments, the mechanicalresonating structure has a thickness T which, in some embodiments, isless than approximately three wavelengths of the resonance frequency ofinterest of the mechanical resonating structure. According to someembodiments, the thickness T is less than approximately 2 wavelengths ofthe resonance frequency of interest. According to some embodiments, thethickness is less than approximately one wavelength of the resonancefrequency of interest (e.g., less than approximately one wavelength of aresonant Lamb wave supported by the mechanical resonating structure).Other thickness values are also possible. According to some embodiments,the thickness of the mechanical resonating structure is betweenapproximately 2-100 times smaller than the length and width of themechanical resonating structure (e.g., 5 times smaller, 10 timessmaller, 50 times smaller, etc.), such that any vibration in thedirection of the thickness may be negligible compared to vibrationapproximately parallel to the length and width. According to someembodiments, the mechanical resonating structures described herein havea large dimension (e.g., length, width, diameter, circumference, etc.)of less than approximately 1000 microns, less than 100 microns, lessthan 50 microns, or any other suitable value. It should be appreciatedthat other sizes are also possible. According to some embodiments, thedevices described herein form part or all of a microelectromechanicalsystem (MEMS).

According to some embodiments, a mechanical resonating structure has awidth corresponding to the direction of secondary vibration of thestructure, and the width has a value that may be chosen in dependence onthe material(s) of which the structure is formed and the desiredresonance frequency of the structure. For example, according to someembodiments, the mechanical resonating structure comprises MN (e.g., asan active layer), and the ratio of the width to the resonant wavelengthof the structure ranges between approximately 0.6-0.9 (e.g., 0.7) orbetween approximately 1.2-1.8 (e.g., 1.5, 1.6, etc.). According toanother embodiment, the mechanical resonating structure comprisessilicon (e.g., as an active layer), and the ratio of the width to theresonant wavelength ranges between approximately 0.6-1.3 (e.g., 0.9,1.1, etc.) or between approximately 1.6-2.2 (e.g., 1.8, 2.0, etc.).According to some embodiments, the ratio of the width of the structureto the resonant wavelength ranges between approximately 0.2-2.5,irrespective of the particular material(s) of which the structure isformed.

According to some embodiments, the mechanical resonating structure mayhave a non-uniform length and/or width. For example, in those situationsin which the mechanical resonating structure is substantiallyrectangular, the width of the structure may vary along the length (i.e.,as a function of position in the direction of the length of thestructure), an example of which is shown in FIG. 7, described below.Similarly, according to some embodiments, the length of the structuremay vary along the width (i.e., as a function of position in thedirection of the width of the structure). In some embodiments, both thelength and width may vary. Such variations of the length and/or widthmay facilitate positioning of the ends and/or sides of the mechanicalresonating structure to substantially align with anti-nodes or nodes ofvibration, at points of minimum displacement, or may be used for anyother reason. According to some embodiments, the length and/or width ofa mechanical resonating structure varies as a function of position, andfacilitates obtaining minimum displacements at the anchor locations.

The mechanical resonating structures may have any desired resonancefrequency or frequencies, as the various aspects described herein arenot limited to use with structures having any particular operating rangeor resonance frequency. For example, the resonance frequency of themechanical resonating structures may be between 1 kHz and 10 GHz (e.g.,between approximately 100 MHz and 150 MHz, between approximately 100 MHzand 3 GHz, or any other suitable values within this range). In someembodiments, the frequencies of operation of the mechanical resonatingstructure are in the upper MHz range (e.g., greater than 100 MHz), or atleast 1 GHz (e.g., between 1 GHz and 10 GHz). In some embodiments, theoutput signal produced by the mechanical resonating structures may havea frequency of at least 1 MHz (e.g., 13 MHz, 26 MHz) or, in some cases,at least 32 kHz. In some embodiments, the operating frequency may rangefrom 30 to 35 kHz, 60 to 70 kHz, 10 MHz to 1 GHz, 1 GHz to 3 GHz, 3 GHzto 10 GHz, or may have any other suitable range.

The mechanical resonating structure may be actuated and/or detected inany suitable manner, with the particular type of actuation and/ordetection depending on the type of mechanical resonating structure, thedesired operating characteristics, or any other suitable criteria. Forexample, suitable actuation and/or detection techniques include, but arenot limited to, piezoelectric techniques, electrostatic techniques,magnetic techniques, thermal techniques, piezoresistive techniques, anycombination of those techniques listed, or any other suitabletechniques. The various aspects of the technology described herein arenot limited to the manner of actuation and/or detection.

According to some embodiments, the mechanical resonating structuresdescribed herein may be piezoelectric Lamb wave devices, such aspiezoelectric Lamb wave resonators. Such Lamb wave devices may operatebased on propagating acoustic waves, with the edges of the structure(e.g., the ends and sides of mechanical resonating structure 102)serving as reflectors for the waves. For such devices, the spacingbetween the edges may define the resonance cavity, and resonance may beachieved when the cavity is an integer multiple of p, where p=λ/2, withλ being the acoustic wavelength of the Lamb wave. However, it should beappreciated that aspects of the technology described herein apply toother types of structures as well, and that Lamb wave structures aremerely non-limiting examples.

As mentioned with respect to FIG. 1, some embodiments include suspendedmechanical resonating structures. The structures may be suspended inthat they may have one or more segments which are not directly attachedto any other structures. For example, in FIG. 1 the ends of themechanical resonating structure are not directly attached to the body.It should be appreciated that various forms of “suspended” structuresmay be used, including, but not limited to, structures having any one ormore free surfaces.

While FIG. 2 illustrates the dimensions of the mechanical resonatingstructure in the absence of surrounding structures, it should beappreciated from reference to FIG. 1 that such mechanical resonatingstructures may be coupled to additional components (e.g., anchors), andthat the additional components may impact the choice of the dimensionsof the structure. For example, the anchors 106 a and 106 b may impactthe vibration of the mechanical resonating structure in the primarydirection, the secondary direction, or in both directions, for exampleby constraining the motion of the sides of the mechanical resonatingstructure. According to an aspect of the technology, a mechanicalresonating structure is dimensioned to minimize the impact of secondaryvibration on primary vibration of the structure, taking into account theconnections of the structure to other elements. For example, accordingto some embodiments, a mechanical resonating structure is coupled to abody (e.g., a substrate) by one or more anchors, and the anchors arepositioned to minimize their impact on the vibration of the mechanicalresonating structure (e.g., to minimize dissipation of the vibration).In some embodiments, the width of the mechanical resonating structuremay be chosen to account for the impact of the anchors on the vibration.In some embodiments, the anchors may be positioned to maximize theirimpact on the vibration of the mechanical resonating structure (e.g., tomaximize dissipation of the vibration).

According to some embodiments, a device comprising a mechanicalresonating structure comprises one or more anchors coupling themechanical resonating structure to a body, and at least one of theanchors contacts the mechanical resonating structure at a point ofminimal displacement of the structure during operation. According tosome embodiments, each of the one or more anchors contacts themechanical resonating structure at a point of minimal displacement ofthe structure during operation. In some embodiments, the mechanicalresonating structure is configured to exhibit primary vibration andsecondary vibration, and the point at which an anchor contacts themechanical resonating structure is approximately on a node of theprimary vibration and/or secondary vibration. For example, referring toFIG. 3A, an anchor may be positioned to connect to the mechanicalresonating structure at the point where the line 302 a terminates on theside 204 b, since that point lies substantially on a node of vibrationin the x-direction and a node of vibration in the y-direction.Similarly, anchors may be positioned where 302 a terminates on side 204a, where line 302 b terminates on side 204 a, and where line 302 bterminates on side 204 b. Such positioning of the anchor(s) may minimizeor eliminate the impact of the anchors on the primary and/or secondaryvibration. According to some embodiments, the anchors contact themechanical resonating structure at points which lie approximately onnodes of both the primary and secondary vibration, and the sides of themechanical resonating structure substantially align with nodes of thesecondary vibration.

It should be appreciated that while two anchors are shown in FIG. 1, andfour potential anchor locations have been described with respect to FIG.3A, that any number of anchors may be used in those embodimentsemploying anchors, and that the technology described herein is notlimited to use with any number of anchors. Thus, according to someembodiments, one or more anchors may be included and may be positionedin any of the manners described above, or in any other suitablelocations.

The dimensions of the mechanical resonating structure according toaspects of the technology described herein may be determined in anysuitable manner. FIG. 4 illustrates one non-limiting example of amethodology by which the dimensions of the mechanical resonatingstructure may be determined. As illustrated, the method 400 isiterative. The iterative loop may be performed any number of times toproduce a desired degree of accuracy, and therefore the methodology 400is not limited to using any particular number of iterations. Inaddition, the method, or any of the sub-steps of the method, may beperformed using any suitable hardware, software, manual calculations, orcombination thereof. Furthermore, one or more of the steps of the methodmay be embodied by software, for example stored on a (non-transitory)computer readable storage medium, which may be executed by one or moreprocessors to perform the steps. According to some embodiments, one ormore of the sub-steps is performed using finite element analysis.

The method 400 begins at 402 with selecting the desired resonancefrequency f_(o). At 404, various parameters of the mechanical resonatingstructure may be set, or assigned. The parameters may include thegeneral geometry of the mechanical resonating structure (e.g.,rectangular, square, or other geometry), the material(s) and/or materialproperties (e.g., stiffness, density, etc.) of the structure, and thethicknesses of the mechanical resonating structure.

At 406, a value of the dimension of the mechanical resonating structurein the direction of the primary vibration to achieve the desiredresonance frequency f₀ may be determined. According to some embodiments,the mechanical resonating structure is substantially rectangular, and isconfigured to exhibit primary vibration in a direction approximatelyparallel to its length. For such non-limiting embodiments, 406 maycomprise determining the length of the mechanical resonating structure.The determination at 406 may be made in any suitable manner, as themethodology 400 is not limited in this respect.

At 408, a value of the dimension of the mechanical resonating structurein a direction of secondary vibration may be determined for the givenresonance frequency f₀, to obtain minimum displacement of the mechanicalresonating structure in this dimension as well as to reduce or preventthe occurrence of unwanted modes of vibration in proximity to f₀.According to some embodiments, the mechanical resonating structure issubstantially rectangular and is configured to exhibit primary vibrationhaving a direction approximately parallel to its length and secondaryvibration having a direction approximately parallel to its width. Forsuch non-limiting embodiments, 408 may comprise determining the width ofthe mechanical resonating structure for the given resonance frequency toachieve minimal or no displacement at the sides of the mechanicalresonating structure and/or to reduce or prevent the occurrence ofunwanted modes of vibration in close proximity to f₀.

At 410, the position(s) of any anchor(s) connected to the mechanicalresonating structure may be determined, such that the impact of theanchor(s) on the primary and/or secondary vibration is minimal. Forexample, the position of the anchors may be chosen so that one or moreof the anchors contacts the mechanical resonating structure at a pointwhich is substantially on a node of vibration for the primary and/orsecondary vibration. According to some embodiments, each of the anchorsis positioned at such a point.

At 412, the value of the dimension in the direction of the primaryvibration determined at 406 may be adjusted to account for any impactthe anchors may have on the operation of the mechanical resonatingstructure (e.g., shifting the resonance frequency of the mechanicalresonating structure or otherwise). Thus, in those embodiments in whichthe dimension from 406 is a length of the mechanical resonatingstructure, 412 may comprise adjusting the determined length to accountfor the anchors.

Similarly, at 414, the value of the dimension in the direction of thesecondary vibration determined at 408 may be adjusted to account for anychanges resulting from the placement of the anchors. In thoseembodiments in which 408 comprises determining a width of the mechanicalresonating structure, 414 may comprise adjusting the width to accountfor the impact of the anchors on the mechanical resonating structure(e.g., on the resonance behavior of the mechanical resonating structureor otherwise).

At 416, a determination is made whether the mechanical resonatingstructure has the desired operating characteristics. While any operatingcharacteristics may be assessed at 416, examples include the resonancefrequency of the mechanical resonating structure, the presence ofunwanted modes of vibration in proximity to the desired resonancefrequency, desired efficiency targets (e.g., Q values), or any othersuitable criteria. According to some embodiments, 416 comprisesdetermining whether any unwanted modes of vibration are too close to thedesired resonance frequency. Whether an unwanted mode is too close tothe desired resonance frequency may depend on the specific applicationin which the mechanical resonating structure is to be used and/or thespecific desired resonance frequency of the mechanical resonatingstructure.

According to some embodiments, the desired operating characteristics ofthe mechanical resonating structure may be met when the sides of themechanical resonating structure align substantially with nodes ofvibration in the secondary direction and when the ends of the mechanicalresonating structure align substantially with anti-nodes of the primaryvibration. However, not all embodiments are limited in this respect. Thedetermination at 416 may be made in any suitable manner, includingexperimentally, using computational methods (software, manual, etc.), orin any other suitable manner.

If, at 416, it is determined that the mechanical resonating structure isappropriately dimensioned such that the mechanical resonating structurehas the desired operating characteristics, the determined dimensions maybe output at 418 and the method may finish at 420. If, on the otherhand, at 416, the mechanical resonating structure is determined to nothave the desired operating characteristics, the method may return to404, and be repeated. In this manner, the method 400 is iterative.

Again, it should be appreciated that any suitable method may be used todetermine the dimensions of the mechanical resonating structure, andmethod 400 is merely one non-limiting example. In addition, each of thesub-processes of method 400 (e.g., 404, 406, 408 . . . ) may beperformed in any suitable manner, as the various aspects describedherein are not limited in this respect.

While FIGS. 1-2 and FIG. 4 provide non-limiting examples of structuresand methods according to some non-limiting embodiments of the technologydescribed herein, it should be appreciated that such structures andmethods may be varied in several respects, without departing from thescope of Applicants' contribution to the art. For example, depending onthe type of mechanical resonating structure at issue, it may include oneor more electrodes. For example, piezoelectric mechanical resonatingstructures may include one or more electrodes for actuation and/ordetection of the operation of the structure. The mechanical resonatingstructures and methods described herein may account for such additionalstructures, to provide a suitably dimensioned and shaped mechanicalresonating structure.

FIG. 5 provides an illustration, showing a portion of a mechanicalresonating structure 502 connected to a body 504 by two anchors, 506 aand 506 b, and including four electrodes 508 a-508 d. According to someembodiments, the electrodes are positioned to minimize their movementduring operation of the mechanical resonating structure. By sopositioning the electrodes, their impact (if any) on the efficiency ofthe resonating structure may be minimized and the electric potentialgenerated by the electrodes may have equipotential lines oriented in adesired manner. For example, one or more of the electrodes may bepositioned to substantially align with the placement of the anchors 506a and/or 506 b. In some embodiments, the anchors and one or more of theelectrodes may be positioned to substantially align with nodes ofvibration in the x-direction (e.g., nodes of primary vibration). Forexample, the centerline of electrode 508 b (the centerline being theaxis of symmetry oriented in the y-direction in FIG. 5) maysubstantially align with a node of vibration of the mechanicalresonating structure in the x-direction. According to some embodiments,the anchor 506 a and/or 506 b is also aligned with the centerline of oneor more of the electrodes.

By positioning the electrodes such that they experience minimal movementduring operation of the resonating structure (e.g., by positioning themsuch that their centerlines substantially align with nodes ofvibration), the lines of electric potential generated by the electrodesmay be substantially parallel to each other. FIG. 6 illustrates anexample of the electric potential corresponding to the resonatingstructure dimensions for FIGS. 3A-3C, with electrodes positioned tocreate absolute maxima of the electric potential at the locations of thevertical black and white stripes. The four arrows indicate the positionsat which anchors may contact the mechanical resonating structure (inthose embodiments that use anchors), and coincide with the absolutemaxima in the non-limiting example of FIG. 6. As can be seen, theelectric potential lines are substantially parallel.

As mentioned above, in some embodiments mechanical resonating structuresmay not have uniform shapes, for example having beveled edges. Suchshapes may optimize operation of the resonating structures, for exampleby facilitating placement of the ends and/or sides of the resonatingstructure to substantially align with anti-nodes or nodes of vibration.FIG. 7 provides a non-limiting example. As shown, the device 700comprises a mechanical resonating structure 702 connected to the body104 by anchors 106 a and 106 b. The mechanical resonating structure 702has a width W_(x) that varies with position along the x-direction (thelength in the non-limiting example of FIG. 7) of the structure. Inparticular, the sides 704 a and 704 b are beveled.

It should be appreciated that the examples described thus far are notlimiting. For example, while multiple examples have described deviceshaving a length and a width and configured to exhibit primary vibrationin a direction approximately parallel to the length and secondaryvibration in a direction approximately parallel to the width, it shouldbe appreciated that in some embodiments devices may be configured toexhibit primary vibration in a direction approximately parallel to awidth of the device and secondary vibration in a direction approximatelyparallel to a length of the device. In some such embodiments, the endsof the device (bounding the length) may substantially align with nodesof the secondary vibration, and the sides of the device (bounding thewidth) may substantially align with anti-nodes of the primary vibration.Other orientations for primary and secondary vibration are alsopossible, as the aspects described herein including primary andsecondary vibration are not limited to applications having anyparticular orientations of primary and/or secondary vibration.

The structures and devices described herein may be used as stand alonecomponents, or may be incorporated into various types of larger devices.Thus, the various structures and methods described herein are notlimited to being used in any particular environment or device. However,examples of devices which may incorporate one or more of the structuresand/or methods described herein include, but are not limited to, tunablemeters, mass sensors, gyroscopes, accelerometers, switches, andelectromagnetic fuel sensors. According to some embodiments, themechanical resonating structures described are integrated in a timingoscillator. Timing oscillators are used in devices including digitalclocks, radios, computers, oscilloscopes, signal generators, and cellphones, for example to provide precise clock signals to facilitatesynchronization of other processes, such as receiving, processing,and/or transmitting signals. In some embodiments, one or more of themulti-port devices described herein may form part or all of a MEMS.

Furthermore, one or more aspects of the invention (e.g., the method ofFIG. 4) may be embodied as a non-transitory computer readable storagemedium (or multiple non-transitory computer readable storage media)(e.g., a computer memory, one or more floppy discs, compact discs,optical discs, magnetic tapes, flash memories, circuit configurations inField Programmable Gate Arrays or other semiconductor devices, or othernon-transitory, tangible computer storage medium) encoded with one ormore programs that, when executed on one or more computers or otherprocessors, perform methods that implement the various embodiments ofthe invention discussed above. The computer readable medium or media canbe transportable, such that the program or programs stored thereon canbe loaded onto one or more different computers or other processors toimplement various aspects of the present invention as discussed above.

The terms “program” or “software” are used herein in a generic sense torefer to any type of computer code or set of computer-executableinstructions that can be employed to program a computer or otherprocessor to implement various aspects of the present invention asdiscussed above. Additionally, it should be appreciated that accordingto one aspect of this embodiment, one or more computer programs thatwhen executed perform methods of the present invention need not resideon a single computer or processor, but may be distributed in a modularfashion amongst a number of different computers or processors toimplement various aspects of the present invention.

Computer-executable instructions may be in many forms, such as programmodules, executed by one or more computers or other devices. Generally,program modules include routines, programs, objects, components, datastructures, etc. that perform particular tasks or implement particularabstract data types. Typically the functionality of the program modulesmay be combined or distributed as desired in various embodiments.

While some references have been incorporated herein by reference, itshould be appreciated that the present application controls to theextent the incorporated references are inconsistent with what isdescribed herein and/or the use of terminology herein.

Having thus described several aspects of at least one embodiment of thetechnology, it is to be appreciated that various alterations,modifications, and improvements will readily occur to those skilled inthe art. Such alterations, modifications, and improvements are intendedto be within the spirit and scope of the invention. Accordingly, theforegoing description and drawings provide non-limiting examples only.

1. A device comprising: a substantially planar mechanical resonating structure having a length and a width, the mechanical resonating structure operable to exhibit primary vibration having a direction approximately parallel to the length of the mechanical resonating structure and secondary vibration having a direction approximately parallel to the width of the mechanical resonating structure, wherein sides of the mechanical resonating structure substantially align with nodes of the secondary vibration for a resonance frequency of the mechanical resonating structure.
 2. The device of claim 1, wherein ends of the mechanical resonating structure substantially align with anti-nodes of the primary vibration for the resonance frequency.
 3. The device of claim 1, wherein the mechanical resonating structure has a substantially rectangular shape.
 4. The device of claim 3, wherein the mechanical resonating structure has one or more beveled edges.
 5. The device of claim 1, wherein a ratio of the width to a resonant wavelength of the mechanical resonating structure is between approximately 0.6-0.9.
 6. The device of claim 1, wherein a ratio of the width to a resonant wavelength of the mechanical resonating structure is between approximately 1.2-1.8.
 7. The device of claim 1, wherein the mechanical resonating structure has an operating frequency ranging from 30 to 35 kHz.
 8. The device of claim 1, wherein the mechanical resonating structure has an operating frequency ranging from 60 to 70 kHz.
 9. The device of claim 1, wherein the mechanical resonating structure has an operating frequency ranging from 100 MHz to 150 MHz.
 10. The device of claim 1, wherein the mechanical resonating structure has an operating frequency ranging from 100 MHz to 3 GHz.
 11. The device of claim 1, wherein the mechanical resonating structure has an operating frequency ranging from 3 GHz to 10 GHz.
 12. The device of claim 1, wherein the mechanical resonating structure comprises a piezoelectric material.
 13. The device of claim 12, wherein the piezoelectric material is chosen from the group consisting of: aluminum nitride (AlN), zinc oxide (ZnO), cadmium sulfide (CdS), lead titanate (PbTiO₃), lead zirconate titanate (PZT), lithium niobate (LiNbO₃), lithium tantalate (LiTaO₃), potassium niobate (KNbO₃), Li₂B₄O₇, langasite (La₃Ga₅SiO₁₄), gallium arsenide (GaAs), barium sodium niobate, bismuth germanium oxide, indium arsenide, and indium antimonide.
 14. The device of claim 1, wherein the mechanical resonating structure is a suspended mechanical resonating structure, and wherein the mechanical resonating structure is coupled to a body by one or more anchors.
 15. The device of claim 14, wherein at least one of the one or more anchors contacts the mechanical resonating structure at a point that lies substantially on a node of the primary vibration.
 16. The device of claim 14, wherein at least one of the one or more anchors contacts the mechanical resonating structure at a point that lies substantially on a node of the secondary vibration.
 17. The device of claim 16, wherein the at least one of the one or more anchors contacts the mechanical resonating structure at a point that lies substantially on a node of the primary vibration.
 18. The device of claim 1, wherein the length is at least one and a half times as large as the width.
 19. The device of claim 1, wherein the sides of the mechanical resonating structure include two sides, and wherein the two sides are each positioned within approximately Λ/5 of a node of the secondary vibration, where Λ is a length of a period of displacement in the direction of the secondary vibration.
 20. The device of claim 19, wherein each of the two sides is positioned within approximately Λ/8 of a node of the secondary vibration.
 21. The device of claim 20, wherein each of the two sides is positioned within approximately Λ/9 of a node of the secondary vibration.
 22. The device of claim 21, wherein each of the two sides is positioned within approximately Λ/12 of a node of the secondary vibration.
 23. The device of claim 1, wherein the substantially planar mechanical resonating structure is a suspended mechanical resonating structure, comprises a piezoelectric material, and is coupled to a substrate by one or more anchors contacting one or more of the sides of the mechanical resonating structure, wherein the mechanical resonating structure is configured to support plate acoustic modes of vibration in which the primary vibration has a magnitude at least two times larger than a magnitude of the secondary vibration, and wherein at least one of the one or more anchors contacts the mechanical resonating structure at a point lying substantially on a node of the primary vibration and a node of the secondary vibration.
 24. The device of claim 1, wherein the mechanical resonating structure has a periphery lying substantially within a first plane, the periphery formed of one or more segments comprising the sides, wherein each of the one or more segments substantially aligns with either a node or anti-node of vibration of a resonance mode of the mechanical resonating structure.
 25. The device of claim 24, wherein the mechanical resonating structure comprises a piezoelectric material.
 26. The device of claim 24, wherein the mechanical resonating structure is configured to support plate acoustic modes of vibration.
 27. The device of claim 24, wherein the mechanical resonating structure has a resonance frequency between approximately 100 MHz and 150 MHz.
 28. The device of claim 1, further comprising an anchor interconnecting the mechanical resonating structure to a body, the anchor positioned to contact a periphery of the mechanical resonating structure at a point positioned approximately on a node of the secondary vibration.
 29. The device of claim 28, wherein the anchor interconnecting the mechanical resonating structure to the body is positioned to contact the mechanical resonating structure at a point positioned approximately on a node of the primary vibration.
 30. The device of claim 28, wherein a largest dimension of the mechanical resonating structure is less than approximately 1000 microns.
 31. The device of claim 30, wherein the mechanical resonating structure is substantially rectangular.
 32. The device of claim 30, wherein the body is a substrate.
 33. The device of claim 32, wherein the substrate has a cavity formed therein, and wherein the mechanical resonating structure is suspended above the cavity.
 34. The device of claim 28, wherein the device comprises a plurality of anchors comprising the anchor, and wherein each of the plurality of anchors contacts the mechanical resonating structure at a respective contact point positioned approximately on a node of vibration of the mechanical resonating structure in the primary direction and on a node of vibration of the mechanical resonating structure in the secondary direction. 